Bring a large pot of water to a boil. Add the broccoli, and cook for five minutes until soft. Using a spatula, transfer the broccoli to a pan over low heat, reserving the water in the pot.
Cook the pasta in the remaining broccoli water according to package directions, reserving at least 1½ cups of the pasta water when you drain.
Now, in the pan with the broccoli, add the olive oil and garlic. Sauté until you can mash up the broccoli, almost into a pesto-like sauce. You can add some water a tablespoon at a time to thin the broccoli floret sauce, as needed.
At this time, add the drained pasta, nutritional yeast, salt, pepper and lemon juice. Stir, adding the reserved pasta water 1/4 cup at a time as needed.